Volume was light as some European markets are closed for the Easter Monday holiday.
"Broader market sentiment was dampened by ongoing trade tensions between the US and China," said Joe Manimbo, senior market analyst, at Western Union Business Solutions in Washington.
China has slapped extra tariffs of up to 25 percent on 128 US products including frozen pork, as well as on wine and certain fruits and nuts, in response to US duties on imports of aluminum and steel, China's finance ministry said.
The tariffs, to take effect on Monday, match a list of potential tariffs on up to $3 billion in US goods published by China on March 23.
The dollar was down 0.2 percent at 89.934 against a basket of six major currencies, backing off from a one-week high of 90.178 set last Thursday.
But the dollar was up 0.1 percent against the yen at 106.24 , after rising more than 1.5 percent last week for its biggest weekly gain since September 2017.
The US currency rose against the yen last week, helped by signs China and the United States were working behind the scenes to avoid a full-blown trade war, as well as hopes for a diplomatic breakthrough over North Korea's nuclear programme.
The dollar's gains versus the yen were viewed as short-lived given the tension between the world's two largest economies.
The Trump administration is expected to release a list of other products to be targeted with tariffs by Friday.
The US move will likely trigger a second round of countervailing penalties from China, which could include strategically-vital product categories such as soybeans and aircraft, Karl Schamotta, director of global product & market strategy at Cambridge FX in Toronto, said.
Beyond the potential trade war, the markets are also focused on US data this week, led by the non-farm payrolls report for March. The reports should determine the path for future interest rate increases, analysts said.
The euro, meanwhile, was little changed at $1.2319.
Although expectations of an exit from the European Central Bank's stimulus had boosted the euro since last year, the common currency has been in a holding pattern since hitting a three-year high of $1.2556 on Feb. 16, with its March 1 low of $1.21545 seen as an immediate support level.